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Solve Question 16

Q.16 (I) find the ratio in which the line segment joining the points (1, 2, 3) and (-3, 4, -5) is divided by the XY-plane.(II) if A and N are the points (-3, 4,-8) and (5, -6, 4) respectively, find the ratio in which YZ- plane divides [AB]. Also find the co-ordinates of the point of section.

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Solution

Dear student
I
Suppose the line joining the points P1,2,3 and Q-3,4,-5 is divided by the xy plane at a point R in the ratio k:1The the coordinates of R are-3k+1k+1,4k+2k+1,-5k+3k+1Since R lies on xy plane i.e. z=0.So,-5k+3k+1=0k=35So, required ratio is 35:1 or 3:5
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